Title says it all. Is there a bitcoin exchange that pays most of fees for you? For example, I want to send Bitcoin to my Electrum wallet but others want to withdraw too. So like my transaction is bundled with many other people's transactions.
The main purpose of exchanges is to generate profits from users. There are alternatives to choose from, but the cost of transportation is limited. Electrum for example. Shipping fees can also vary. We are all aware of the increased fees recently. We had to wait for the transfer, so I don't think what you want is very possible. You just have to wait for the right time. Unless you're in a hurry.
You can also use other coins if you're in a hurry when there's congestion on Bitcoin network but you want the transaction faster and don't wan to pay high fees because you don't have the money for that then you can withdraw with stablecoin and spend those instead of your Bitcoin. Asking exchange to pay for your fees or others to do that for you won't be possible because exchange are business and they have other expenses to take care of.
The only thing I know an exchange can do for you is to remove their trading fees that they charge for each trade done on the exchange, they can remove the trading fees because they're the ones receiving the trading fees but for withdrawal fees, it's the miners been paid.